1420 0 obj<>stream <]>> 0000003948 00000 n For a major accident, the policy pays \$5000; for a minor accident, %PDF-1.6 %���� Expected value = Number of experiments × Probability = N × p = 30 × 0.25 = 7.50. 0000022036 00000 n Here is a “solution.” startxref calculating the expected monetary values of all alternatives, and selecting the alternative with the highest expected monetary value. 0000003333 00000 n 89 23 Find the probability that x = 2. b. This term has been retained in Problem 7.2.4 Solution From De nition 3.6, the PDF of Y is E(X) = µ. Find out the expected value of its outcomes. Total experiments (N) = 30. 0 For each of the following probability distributions, calculate the expected value and standard deviation: a. Therefore, the expected value of getting blue ball is approximately 8. 0000000016 00000 n Solution xref 0000002012 00000 n X takes on what values? 4 Chapter 3: Decision theory be interpreted as the long-run relative frequencies, and theexpected payo ﬀ as the average payo ﬀ in the long run. xref 0000003589 00000 n X and Y are dependent), the conditional expectation of X given the value of Y will be diﬀerent from the overall expectation of X. Solutions to risk and return practice problems 1 . side. 0000002905 00000 n +p(On)Xn The expected value is often denoted just by E. 8 Calculating Expected Value E = + + = 11 1 273 15()-42 4 4 − Make a table like this one Outcome Probability Value of X HH 1/4 7 HT or TH 1/2 3 TT 1/4 -15 O1 O2 O3 X1 X2 X3. Risk measurement 1. The determina-tion of the optimal alternative becomes a little more complicated when the alternatives involve sequences of decisions. 0000003272 00000 n endstream endobj 1443 0 obj<>/W[1 1 1]/Type/XRef/Index[56 1361]>>stream Example 6.17. A. Example 1: Researchers have conducted a survey of 1600 co ee drinkers asking how much co ee they drink in order to con rm previous studies. 0000006050 00000 n (3) The variance is then Var[Y]=E[Y2]−E[Y]2 =2−(4/3)2 =2/9. The expected value of the random variable X is, by definition: E(X) = p(O1)X1 + p(O2)X2 +p(O3)X3 + …. 4. c 2013 by Henk Tijms, Vrije University, Amsterdam. 0000079279 00000 n 0000079882 00000 n Probability Exam Questions with Solutions by Henk Tijms1 December 15, 2013 This note gives a large number of exam problems for a ﬁrst course in prob-ability. ���s��6?Y��V#P9l`�'��R؃K�ӽ�N��_�RV*�yU���[���\��C�X��9�Ɂ�KzN�ْ�P�+��YJ����� � �V"�P�uw��0l0 Choose, at random, three points on the circle x2 + y2 = 1. We often refer to the expected value as the mean, and denote E(X) by µ for short. 0000009547 00000 n 111 0 obj <>stream 0000004694 00000 n Expected value Investment problem: • You have 100 dollars and can invest into a stock. 0000008829 00000 n Outcome Probability 2Outcome value px x-E(x) (x-E(x))2 p(x-E(x)) Good 30% \$40 \$12\$16\$256 77 Normal 50% \$20 \$10-\$4\$16 8 Bad 20% \$10 \$2-\$14\$196 39 100% E(x) = \$24 variance = 124 standard deviation = \$11 b. Probability of getting a blue ball = (p) = 1/4 = 0.25. Expected Value Deﬁnition 6.1 Let X be a numerically-valued discrete random variable with sam-ple space Ω and distribution function m(x). (vii)Reject H 0 if ˜2 is larger than the critical value (right-tailed test). trailer 0000010277 00000 n Find the sum of the elements of S. The next three problems are harder; in these problems linearity of expectation is not the main idea of the solution. 0000003747 00000 n 0000006738 00000 n 0000008097 00000 n 0000001306 00000 n Find the expected value of S. Problem 2.5 (AIME 2006 #6). 18. First-step analysis for calculating the expected amount of time needed to reach a particular state in a process (e.g. the formula of expected value, and compute the expected value of a game, Statistics and Probability, how to find expected value of an event, Conditional probability and expected values, examples and step by step solutions, HSS-MD.A.3, random variable, expected value 0000022357 00000 n These problems will tend to be of the repetitive kind, so that the probabilities may.